Speedups of linearly recurrent subshifts

TL;DR

This paper proves that applying a homeomorphic speedup to a linearly recurrent two-sided subshift results in another linearly recurrent subshift, extending understanding of the structure of such dynamical systems.

Contribution

It establishes that the property of linear recurrence is preserved under homeomorphic speedups in two-sided subshifts.

Findings

Homeomorphic speedups preserve linear recurrence.

Linearly recurrent subshifts remain linearly recurrent after speedup.

Applicable to primitive substitution and Sturmian shifts.

Abstract

A speedup, like a time change in discrete time dynamics, is a way of moving faster through the orbits of a dynamical system. Linearly recurrence is a stronger form of minimality for subshifts, shared by e.g.\ all primitive substitution shifts and Sturmian shifts associated with rotation numbers of bounded type. We prove that the homeomorphic speedup of a linearly recurrent two-sided subshift is again linearly recurrent.